Calculator Inputs
Example Data Table
| Example | Point 1 | Point 2 | Δx | Δy | Distance | Midpoint |
|---|---|---|---|---|---|---|
| Example 1 | 3 + 4i | -1 + 2i | -4 | -2 | √20 ≈ 4.4721 | 1 + 3i |
| Example 2 | 1 - 2i | 4 + 6i | 3 | 8 | √73 ≈ 8.5440 | 2.5 + 2i |
| Example 3 | -5 + i | 2 - 3i | 7 | -4 | √65 ≈ 8.0623 | -1.5 - i |
Formula Used
Rectangular forms: z₁ = x₁ + y₁i and z₂ = x₂ + y₂i
Distance: |z₂ − z₁| = √[(x₂ − x₁)² + (y₂ − y₁)²]
Squared distance: d² = (x₂ − x₁)² + (y₂ − y₁)²
Midpoint: M = ((x₁ + x₂)/2) + ((y₁ + y₂)/2)i
Polar conversion: x = r cos(θ), y = r sin(θ)
The calculator first converts each point to rectangular coordinates. It then measures separation on the complex plane using the Euclidean formula. Extra outputs, such as midpoint, translation vector, arguments, and modulus change, support deeper review and checking.
How to Use This Calculator
- Choose rectangular or polar entry for each point.
- Enter real and imaginary parts, or modulus and angle.
- Pick degrees or radians for all angle-based inputs.
- Set the decimal precision you want in results.
- Press Calculate Distance to show the report above the form.
- Review distance, exact form, midpoint, translation vector, and phase values.
- Use the CSV or PDF buttons to export the current result set.
FAQs
1) What does complex distance measure?
It measures the straight-line separation between two complex numbers on the Argand plane. The result is always a real, non-negative value.
2) Can I mix rectangular and polar inputs?
Yes. Each point can use its own mode. The calculator converts both values to rectangular form before applying the distance formula.
3) Why is squared distance included?
Squared distance avoids the square root and is helpful in algebraic proofs, optimization work, and comparisons where exact ordering matters more than the final unit length.
4) What is the midpoint used for?
The midpoint shows the exact center of the segment joining the two complex points. It is useful in geometry, transformations, and visual checking.
5) Should I choose degrees or radians?
Choose the unit that matches your source data. Degrees are common in classroom work, while radians are often preferred in higher mathematics and technical analysis.
6) Why do polar entries sometimes create tiny decimals?
Trig conversions can produce very small rounding values, such as 0.0000 instead of zero. The formatter trims these values for cleaner output.
7) Do the export buttons save the current results only?
Yes. CSV and PDF exports use the currently displayed report. Recalculate first if you change any inputs and need updated files.
8) Is this calculator suitable for study and verification?
Yes. It is designed for practice, homework checking, demonstrations, and quick validation of manual work involving complex-plane geometry.